Phonon Thermal Edelstein Effect*

Spin-rotation coupling in crystals enables us to convert between spin current and mechanical rotations. In this presentation, we focus on the angular momentum of phonons. When the temperature gradient is applied to nonmagnetic crystals without inversion symmetry, the phonon angular momentum is proportional to temperature gradient. This mechanism is analogous to the Edelstein effect in electronic systems. This effect requires crystals with sufficiently low crystallographic symmetries. We calculate the phonon angular momentum generated by temperature gradient in wurtzite-GaN and tellurium by first-principle calculation. Moreover we propose that the phonon angular momentum is converted to a rigid-body rotation of crystals and the magnetization. On the other hand, in magnetic crystals, we discuss the dependence of the phonon angular momentum on magnetic symmetries.